1. The probability of a 7 is 1/6 since out of 36 combinations the 6 combinations that give 7 are 1-6, 2-5, 3-4, 4-3, 5-2, 6-1. The probability of not getting a 7 on a roll is 5/6. The probability of not getting 7 for n rolls is (5/6)^n. This becomes less than .5 for n = 4 rolls.


2. This is intended to be a trick. The probability of being right if you predict it will hit on the nth play is the probability that it will not hit on the first n-1 plays and then hit on the nth play. This is

(1/40,000)(39999/40000)^n. This is maximum for n=1, so you should predict it will happen on the first play for the prediction to have the highest probability of being right.


This is not the same thing as asking how long it will take to have a greater than 50% chance of hitting as we did in the first problem, nor is it the same as asking the average time it will take. It also doesn't matter that the machine just hit as long as the machine has no memory.